The proposed research is motivated by problems arising in the statistical design and analysis of cancer clinical trials. In each trial, outcome-adaptive decisions are made repeatedly as the trial progresses and the data from patients treated previously in the trial become available. Possible decisions include choosing a patient's dose or treatment, dropping a treatment, stopping the trial, adaptive randomization, and selecting an optimal treatment or multi-course treatment strategy. Because outcome-adaptive methods use more available information on a more timely basis, they are more scientifically valid and more ethical. At each interim analysis, the underlying model must be re-fit and decision criteria re-computed, which requires either updating the posterior under a Bayesian model, or computing a test statistic under a frequentist model. We evaluate average design behavior by computer simulation, which requires the interim decision criteria to be computed many times. Consequently, the proposed methods are computationally intensive. We also will apply more formal criteria, including Bayesian A-, D-, or T-optimality and decision theoretic methods. Depending on the application, the trial may involve various types of multiplicities, including multivariate outcomes, multiple disease subtypes, multiple treatments, or multiple courses of treatment per patient. We will explore and apply Bayesian regression models, hierarchical models, and latent variable models to accommodate these multiplicities and account for heterogeneity and association. Proposed research projects include developing models, methods and designs for (1) Dose-finding in clinical trials where the doses of two agents are varied, with the goal to find several acceptable dose pairs; (2) Dose finding in clinical trials where patient outcome is a multivariate ordinal variable representing several qualitatively different toxicities having different clinical importance; (3) Clinical trials in diseases with multiple subtypes; (4) Evaluating treatment effects on a disease presenting in multiple body sites in each patient; (5) Carrying out both dose-finding and treatment selection with multiple treatments; (6) Accounting for patient heterogeneity in Bayesian models when clinical outcome is multinomial; and (7) Frequentist selection and testing designs based on a bivariate outcome including response and toxicity. In order to promulgate the methods to the statistical and medical communities, user-friendly computer software for implementation will be made freely available.